Search Research Symposium Abstracts

Mapping Class Groups of Infinite Graphs

Recently, Algom-Kfir and Bestvina introduced mapping class groups of locally finite graphs as a proposed analog of the outer automorphism group of a free group in the infinite-type setting. In this talk, we will introduce infinite-type graphs, their mapping class groups, and why we consider these to be the "big" analog of Out(F_n). Using a [Read More...]

Presenter: Hannah Hoganson, University of Maryland
Authors: George Domat, Sanghoon Kwak
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: September 30, 2023; 9:45 am

Fine curve graphs and the mysterious part of Homeo(S)

The fine curve graph of a surface S was introduced by Bowden–Hensel–Webb in 2019 to study the diffeomorphism group of S. This talk will be a brief introduction to the world of variants of fine curve graphs and a survey of recent results. The results mentioned will include work joint with Katherine Booth, Ryan Dickmann, and Daniel [Read More...]

Presenter: Roberta Shapiro,
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: September 30, 2023; 10:10 am

Thin Surface Subgroups of Arithmetic Lattices in $\textrm{SO}(4,1)$

Representations of surface subgroups in semi-simple Lie groups have been a rich area of research in recent years. In 2009 Kahn and Markovic solved the surface subgroup conjecture for hyperbolic 3-manifolds by constructing thin representations of surface subgroups in lattices in $\textrm{SL}(2,\mathbb{C})$. Additionally, there have been several other new [Read More...]

Presenter: Sara Edelman-Munoz, Rice University
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: September 30, 2023; 10:35 am

Arithmetic Dynamics on Character Varieties

If G is a reductive algebraic group over Z, the G-character variety of a finitely presented group, F parameterizes the set of closed conjugation orbits in Hom(F, G). In this talk, we explore the dynamics of the action of the group of outer automorphisms, Out(F), on the finite field points of the character variety X_F(G) . We define groups of free-type as [Read More...]

Presenter: Cigole Thomas, Colorado State University
Authors: Cigole Thomas
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: September 30, 2023; 11:00 am

Homology of regular finite covers of graphs

There has been recent interest in determining which sets of curves on a possibly punctured surface S, when lifted, generate the homology of every regular finite cover of S; there is an analogous question for regular finite covers of graphs. Work of Malestein and Putman shows that for any punctured S of sufficient genus, the rational homology of some regular [Read More...]

Presenter: Becky Eastham, University of Wisconsin-Madison
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: October 1, 2023; 9:45 am

Parabolic Subgroups of Artin Groups

Parabolic subgroups are an important tool for studying the properties of Artin groups. One fundamental question is whether the intersection of a set of parabolic subgroups is itself a parabolic subgroup. This question is open in the general case, but is known to be true for many subclasses of Artin groups, including braid groups, right-angled Artin groups, [Read More...]

Presenter: Jill Mastrocola, Brandeis University
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: October 1, 2023; 10:10 am

One-endedness of outer automorphism groups of free products of finite and cyclic groups

Freudenthal and Hopf introduced the notion of ends of groups and spaces and proved that a finitely generated group has 0, 1, 2, or infinitely many ends. Later Stallings proved that a finitely generated group has more than one end if and only if it acts minimally on a tree with finite edge stabilizers, so being one-ended is in some sense generic. We [Read More...]

Presenter: Rylee Alanza Lyman, Rutgers University–Newark
Authors: Rylee Alanza Lyman
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: October 1, 2023; 10:35 am

Discussion about the Research Postdoc Application Process

A casual discussion about the process of applying to research postdoctoral positions in theoretical [Read More...]

Presenter: Hannah Hoganson, Rylee Lyman, University of Marlyland
Symposium Year: 2023
Session: Women in Groups, Geometry, and Dynamics [Organized by Hannah Hoganson and Rylee Lyman]
Presentation Time: October 1, 2023; 11:00 am